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Math Help - Harry's Discount

  1. #1
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    Harry's Discount

    Hi,

    I need the reasoning behind the answer for this question explained, please.

    At Harry’s Discount Hardware everything is sold for 20% less than the price marked. If Harry buys tool kits for $80, what price should he mark them if he wants to make a 20% profit on his cost?

    The answer given is $120.

    My reasoning was to find 20% of 80 then subtract it from 80, then add it back and the answer would be 80. Upon recognizing the abject failure of this attempt I reasoned it another way: he wants to make a 20% profit and the discount for everything would be 20%, so I found 40% of 80, 32, and added it to 80. The answer equaling $112. I used 40% because splitting it in half gives 20 a piece. One of the 20%'s is the profit and the other is the discount.

    In truth my understanding of the question is a little murky and my reasoning skills are unenviable.
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  2. #2
    Pim
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    Okay, the problem with percentages is, that you can't just "split them in half". Percentages are relative to something. In this case, the 20% discount is relative to the pricetag, while the 20% profit is relative to the $80 Harry buys toolkits for.

    So, he wants to make 20% profit.
    This means he wants to receive 0.20*80+80=$96
    This does not yet include the discount.
    Then he wants to price it as such, that once the discount is calculated, what is left over is $96.
    This means $96 is equal to 80% (100%-20%)

    Therefore you need to solve 0.80*x=$96, and x is the price that goes on the price tag.

    Does this make it clear?
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  3. #3
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    I get the first part. Though I wonder if the discount could have been found first.

    Quote Originally Posted by Pim View Post
    This means $96 is equal to 80% (100%-20%)

    Therefore you need to solve 0.80*x=$96, and x is the price that goes on the price tag.

    Does this make it clear?
    I'm not understanding this part. Why did you subtract 20% from 100%? I'm not entirely sure how you arrived at the equation. Division seems a good choice but I don't understand why. I multiplied 96 by 0.80, result never made sense. Added 20% of 80 to 96, 112, made sense (only because 112 is an answer option). Essentially I'm just guessing.
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  4. #4
    Pim
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    So, my reasoning was the following:

    You have the pricetag that Harry puts on the tool kit. Let's call this price "x". Now, a customer walks in, and he sees the sign "Everything 20% off". Therefore if he sees a pricetag of $100, he expects to pay $80. (This is how percentages are relative.)
    Now, the customer sees the price tag of "x". x must be chosen as such that he expects to pay $96. (This way Harry makes his 20% profit.)
    Therefore, the price x, can be split in two parts: 80% is the price he actually pays ($96), 20% is the discount.

    Normally, if you calculate a percentage of something, you can multiply by the percentage divided by hundred. Therefore, the price (x) multiplied by 80/100 (0.8) should be equal to $96

    I don't know how much experience you have with solving equations. So, I'm going to teach you a relatively simple, but un-mathematical trick.

    So, you know 0.80*x=$96
    You can compare this to 2*3=6
    You know that 3 = 6/2
    Therefore, x = $96/0.80 = $120

    I hope this answers your question, if not, don't hesitate to ask about anything that's unclear.
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  5. #5
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    Yeah, I feel more comfortable with it now. Thank you.
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